Problem: $ E = \left[\begin{array}{rrr}2 & 2 & 3 \\ 4 & 2 & -1\end{array}\right]$ $ D = \left[\begin{array}{rrr}4 & -1 & -1 \\ -1 & 4 & 1\end{array}\right]$ Is $ E- D$ defined?
Answer: In order for subtraction of two matrices to be defined, the matrices must have the same dimensions. If $ E$ is of dimension $( m \times  n)$ and $ D$ is of dimension $( p \times  q)$ , then for their difference to be defined: 1. $ m$ (number of rows in $ E$ ) must equal $ p$ (number of rows in $ D$ ) and 2. $ n$ (number of columns in $ E$ ) must equal $ q$ (number of columns in $ D$ Do $ E$ and $ D$ have the same number of rows? Yes Yes No Yes Do $ E$ and $ D$ have the same number of columns? Yes Yes No Yes Since $ E$ has the same dimensions $(2\times3)$ as $ D$ $(2\times3)$, $ E- D$ is defined.